Solving: $\frac{d}{dx}\left(y=\frac{7x+1}{8x-2}\right)$
Exercise
$\frac{dy}{dx}\left(y=\frac{\left(7x+1\right)}{\left(8x-2\right)}\right)$
Step-by-step Solution
Learn how to solve properties of logarithms problems step by step online. Find the implicit derivative d/dx(y=(7x+1)/(8x-2)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify the product -(7x+1).
Find the implicit derivative d/dx(y=(7x+1)/(8x-2))
Final answer to the exercise
$y^{\prime}=\frac{-11}{2\left(4x-1\right)^2}$